# NUMERICAL ANALYSIS + MATLAB (Assignment)

only “one” page report

in the assignment attached, there is a demo for matlab

this is the demo:

Gaussian Elimination in floating point arithmetic

*((here is the code for this part for matlab)):

```% Class: MACM 316_x000D_
% Title: Gaussian Elimination for a random matrix demo_x000D_
% Description: Computes the mean solution error over Ntr trials for the_x000D_
% system Ax=b where A is a random NxN matrix and x is a vector of ones._x000D_
% Plots the result as a histogram._x000D_
% File name: LSRandom.m_x000D_
_x000D_
N = 10; % Matrix size_x000D_
Ntr = 100; % Number of trials_x000D_
_x000D_
errs = zeros(Ntr,1); % Vector of errors_x000D_
x = ones(N,1); % exact solution vector_x000D_
_x000D_
for i=1:Ntr_x000D_
_x000D_
A = randn(N,N); % Construct a random NxN matrix (normally distributed)_x000D_
b = A*x; % Compute the right-hand side vector_x000D_
z = Ab; % Solve the linear system_x000D_
_x000D_
errs(i) = max(abs(z-x)); % Compute the error_x000D_
end_x000D_
_x000D_
% Compute the mean and standard deviation of the error_x000D_
mean_err = mean(errs)_x000D_
sdev_err = sqrt(var(errs))_x000D_
_x000D_
% Plot a histogram of the errors_x000D_
hist(log10(errs),10)_x000D_
title(['histogram of log_{10}(error) for ' num2str(Ntr) ' solves with a ' num2str(N) 'x' num2str(N) ' matrix'],'fontsize',14)_x000D_
xlabel('log_{10}(error)','fontsize',12)_x000D_
ylabel('number','fontsize',12)```